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Spatially-periodic patterns are studied in nonlocally coupledGross-Pitaevskii equation. We show first that spatially periodic patternsappear in a model with the dipole-dipole interaction. Next, we study a modelwith a finite-range coupling, and show that a repulsively coupled system isclosely related with an attractively coupled system and its soliton solutionbecomes a building block of the spatially-periodic structure. That is, thespatially-periodic structure can be interpreted as a soliton lattice. Anapproximate form of the soliton is given by a variational method. Furthermore,the effects of the rotating harmonic potential and spin-orbit coupling arenumerically studied.

Soliton lattices in the Gross-Pitaevskii equation with nonlocal and repulsive coupling